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Properties of hydraulic fluids, such as density or viscosity, are usually tabulated (or expressed by analytical formulas) as functions of pressure and temperature. In order to justify the choice of pressure and temperature as independent variables, the Gibbs' phase law of thermodynamics should be considered:

(2.1)

The Gibbs' rule defines the number of degrees of freedom, f, necessary to describe the state of a substance in thermodynamic equilibrium. The formula uses the number of components of the substance (n) and the number of phases in equilibrium (κ). The number of degrees of freedom is the number of independent intensive variables that can be varied simultaneously and arbitrarily without determining one another. An intensive variable does not depend on the size of the considered system. For the case of a hydraulic oil, specific volume, density, pressure, temperature, and viscosity are examples of intensive variables.

If we consider the hydraulic fluid as a single component matter (i.e. a pure chemical) even if it is usually a mixture of different components, then from Eq. (2.1), for a single‐component system (n = 1) in the liquid phase (κ = 1), the number of degrees of freedom f is equal to two. This means that two intensive variables can be arbitrarily selected to completely determine the status of the fluid. Among all possible choices, choosing pressure and temperature is particularly convenient because:

 pressure and temperature are relatively easy to measure, with respect to other intensive properties of the fluid; and

 an engineer has a better ability or practical intuition to relate pressure and temperature to practical problems.

Two intensive variables fully define the status of a liquid. In hydraulic, pressure and temperature are the typical choice for the independent variables used to express the functional between fluid properties.